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On the structure of A-free measures and applications
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de Philippis, Guido and Rindler, Filip (2016) On the structure of A-free measures and applications. Annals of Mathematics, 184 (3). pp. 1017-1039. doi:10.4007/annals.2016.184.3.10
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Official URL: https://doi.org/10.4007/annals.2016.184.3.10
Abstract
We establish a general structure theorem for the singular part of A-free Radon measures, where A is a linear PDE operator. By applying the theorem to suitably chosen differential operators A, we obtain a simple proof of Alberti’s rank-one theorem and, for the first time, its extensions to functions of bounded deformation (BD). We also prove a structure theorem for the singular part of a finite family of normal currents. The latter result implies that the Rademacher theorem on the differentiability of Lipschitz functions can hold only for absolutely continuous measures and that every top-dimensional Ambrosio–Kirchheim metric current in Rd is a Federer–Fleming flat chain.
| Item Type: | Journal Article | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Radon measures, Differential equations, Partial | ||||||||
| Journal or Publication Title: | Annals of Mathematics | ||||||||
| Publisher: | Mathematical Sciences Publishers | ||||||||
| ISSN: | 0003-486X | ||||||||
| Official Date: | 16 September 2016 | ||||||||
| Dates: |
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| Date of first compliant deposit: | 6 May 2016 | ||||||||
| Volume: | 184 | ||||||||
| Number: | 3 | ||||||||
| Page Range: | pp. 1017-1039 | ||||||||
| DOI: | 10.4007/annals.2016.184.3.10 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Funder: | Italy. Ministero dell'istruzione, dell'università e della ricerca (MIUR), Engineering and Physical Sciences Research Council (EPSRC) | ||||||||
| Grant number: | RBSI14RVEZ (MIUR), EP/L018934/1 (EPSRC) | ||||||||
| Open Access Version: |
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